By his inviting a foreign leader to address Congress, John Boehner deliberately dealt in foreign policy and thus violated the "Logan Act", thus usurping the powers of the presidency of the United States. In so doing, Boehner also deliberately violated the "separation of powers" clause in the US Constitution.
By law, he must now be tried by Congress, and forced to resign.
Under the "Logan Act" of 1799, (1 Stat. 613, 30 January 1799, currently codified at 18 U.S.C. § 953) Executive power to engage in Foreign Policy is ONLY vested in the President of the United States of America. The Logan Act specifically forbids any unauthorized citizens from negotiating and interfering in relations between the United States and foreign governments. It was passed in 1799 and last amended in 1994.